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Homework Help: Formula question

  1. Aug 7, 2005 #1
    This isn't a homework question, but I'm just wondering how the text in the book gets from one formula to the next.

    To figure out total kinetic energy of a rotating object:

    K translational + K rotational

    [tex]\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2[/tex]

    Then the book gives an alternate formula:

    [tex]\frac{1}{2}mv^2(1+\frac{I}{mr^2})[/tex]

    So I wanted to see how they get from one to the other. So I tried

    [tex]\frac{1}{2}mv^2+\frac{1}{2}I (\frac{v}{r})^2[/tex]

    factor out the 1/2v^2

    [tex]\frac{1}{2}v^2 (m+\frac{I}{r^2})[/tex]

    almost there. But how do I get a 1 in place of the m? I could divide by m, but then I get

    [tex]\frac{v^2}{2m} (1+\frac{I}{mr^2})[/tex]

    It works for the right term, but not the left. What am I doing wrong?
     
  2. jcsd
  3. Aug 8, 2005 #2

    Fermat

    User Avatar
    Homework Helper

    You just didn't factor out completely.

    You ended up with,

    [tex]\frac{1}{2}v^2 (m+\frac{I}{r^2})[/tex]

    now take out m. i.e. divide both terms inside the brackets by m so that you end up with m outside the barckets.

    Alternatively, you could multiply out the alternate formula, and you will end up with the original one.
     
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